Sunday, May 22, 2016

The Assessment Trap, Part 3: The Meaning of Grades

(This is a slightly edited version of a post from 2011)

Previous posts [Part 1, Part 2] have focused on the uses of assessment. For many students, parents, teachers, and administrators the key purpose of assessment is to assign grades. Before going any further, we need to think about the meaning of grades.

Grades have no intrinsic, absolute meaning. An A at an elite private school does not mean the same thing as an A at a public school that serves a poor neighborhood. An A at my own school today does not mean the same thing as an A meant 20 years ago. An A in Science does not mean the same thing as an A in History. And on it goes. The one feature of grades that is quite reliable is that an A in a given department at a given school is better than a B, which in turn is better than a C. In other words, the meaning of grades is relative. They are how we compare students to each other.

Almost all teachers will fix how they compute their grades if the outcome does not sort the students correctly. If a student deserves an A, and your calculation yields a B, you will find a way to tweak the percents, or the scores, or the participation points, or the extra credit, or something, to make sure the student does not get cheated by a pseudo-objective algorithm. (Admittedly, if the calculations yield an A, rather than the B we expected for a given student, most of us would let it be.) This makes sense, because teaching is as much an art as a science. Given a small enough class and enough of the right sort of contact with the students, a competent teacher knows better how to sort the students than any formula. (Yes, better assessments yield more accurate grades — that’s what I meant by “the right sort of contact”.)

In the rare case of the teacher who delivers much worse or much better grades than expected by their school, they will be taken aside by an administrator, and told that their practice is out of line. This does not require looking at the students’ work — it is more evidence that grades are strictly a relative measure.

In short, grades compare students to each other. They have no other meaning. This is why colleges are interested in grades. If grades were not about sorting students, they would be useless. Just to be clear: grades do not compare students only to others in the same section of the same class, but with the somewhat broader group of students in the same cohort at the same school. And moreover, it is of course true that the rankings are only meaningful if you accept the teacher's and the school's assumptions and values.

One might argue that grades are a measurement of how well a student meets the standards of a given class. This is true enough, but the standards in question only exist in relation to the specific students currently enrolled at the school. If almost every student met a given set of standards, no matter how valid those are, it could not and would not be used as a way to assess achievement in the class and determine the grade. In fact, such a set of standards would make for a course that is too easy for the given population. Conversely, a set of standards that is met by almost no one makes for too difficult a course. The only standards worth aiming for are precisely the ones that sort students into A, B, C bins.

Some will maintain that this is an argument against a system with no grades at all. Without grades, it would be easier to set your expectations too high or too low, or to have a bimodal distribution, with some students doing very well, others clueless, and little in between. Giving grades can help us calibrate challenge and access in the classes we teach. In other words, giving grades is not per se wrong. In fact, it can be useful.

But that does not negate this fact: grades are about comparing students to each other. Students know it, parents know it, teachers in practice know it. Educators who believe otherwise are deceiving themselves.

2 comments:

Henri, thank you again for coming out to do your summer workshop on our Head-Royce campus. May the learning never stop! I find myself agreeing with the many points you make about assessments and grades in your blog series. Regarding this post in particular, I am struggling to agree that grades are ONLY about comparing students to each other. To some extent, grades can help students compare their current selves to their previous selves. A student who receives Cs in 9th grade math, Bs in 10th grade math, and As in 11th grade math has likely made significant progress as a math student (assuming there was some degree of consistency among members of the math department.) More importantly, I like to think that grades can summarize how my students performed against absolute standards of scholarship. If I select a finite set of conceptual understandings, math skills, and problem-solving dispositions, then I can strive to create assessments that measure student progress in these areas. For example, a student can score 95/100 points on my Logarithms test regardless of what any other student scores. In fact, my student can score 95/100 even if no other student takes the test. Furthermore, ALL of my students could conceivably score 95/100 pts. When I publicly post to parents and colleges that all of my students received an "A", then I am not using grades to rank students, at least not in a way that helps the sorting process. Rather, I am comparing each of them to my absolute standard of mastery in the area of logarithms. Sure, the colleges might later compare my "A" student at Head-Royce to an "A-" students at Urban School, but I the teacher am not using grades to compare or rank students.At least, this is what I think I am doing. Am I mistaken or naive in my use of grades?

If your students all always get A's in a certain course, you are probably not challenging them enough. It is almost certain that if you covered more material, or gave harder problems, some of your students would do a lot better than others, and it would be impossible to justify giving the same grades to all of them. If on the other hand you didn't cover more material or give harder problems, you're robbing your stronger students, and in fact all your students because you're not stretching them or giving them something to aspire too.

Your belief that there is an objective 95% on a logarithm test makes no sense to me. The same test could have questions weighted differently, or have partial credit assigned differently, or have more of this type of question and less of that kind, and so on. Even if that were not the case, one could argue that your test is too easy or too hard -- that is strictly a matter of context and selection of goals. One teacher may think that students correctly switching to another base via a memorized formula is important in Algebra 2, another teacher may think it's fine to use any base as long as it makes sense to the student and they can apply it to real world problems, a third teacher may not have an opinion this, and just want their students to be able to answer SAT questions about logs. The same test would yield different results in each of these teachers' classes. Just because you give a percent score doesn't make it scientific. Grading is extremely subjective, though it almost certainly reflects how you see your students.

Finally, if _all_ Mr. X's students were _consistently_ getting C's, or A's, most administrators would think something is wrong. It can happen on one test, but not throughout a course. Mr. X would be under pressure to change their teaching, or their assessments, or the way they arrive at the grade, so that the grades can be used to compare the students.

Still, you're right, grades can indeed help see a student's progress. But I don't think that can be separated from the reality that they are strictly a relative measure.

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Henri Picciotto

I have retired from the classroom after 42 years as a math teacher in K-12 — from counting to calculus. I now work with teachers and schools, and I continue to develop curriculum.

I share instructional materials on my Math Education Page, and my views on math education on this blog. Also on this blog, announcements about: new pages, updates, etc. on the site; my publications; my appearances at conferences; and my other activities in math education.

--Henri

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All the comments between August 2013 and June 2016 got deleted at once by Google when I disconnected the comments from Google+. I had to disconnect because otherwise it was impossible to remove spam. Apologies to all the commenters.